Dynamically adjusted brush for direct paint systems on parameterized multi-dimensional surfaces

ABSTRACT

A system that implements a “tangent space brush,” allowing a user to paint directly onto a parameterized object, for example a three dimensional object. A tangent space brush projects coordinates from an input device to the world-space point on the surface of the 3D object. A normal is determined at that point and a brush image is projected from that point, along the normal, to the underlying surfaces. The system is implemented by providing a system that implements selecting a selected area of a displayed object, and projecting a brush directly onto a surface of the selected area.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application is related to and claims priority to U.S. patentapplication Ser.No. 09/998,919, entitled “Dynamically Adjusted Brush ForDirect Paint Systems On Parameterized Multi-Dimensional Surfaces,” byMaillot et al, filed Dec. 3, 2001, and U.S. provisional applicationentitled, “Dynamic Brush Plane: An Easy Way to Apply Image ProcessingTechniques to 3D Shapes,” having Ser. No. 60/306,153, by Maillot et al.,filed Jul. 19 2001, and incorporated by reference herein. Thisapplication also incorporates by reference the U.S. patent entitled,“Method, System, and Computer Program Product for Updating Texture WithOverscan,” US. Pat. No. 6,037,948, by Liepa, granted Mar 14, 2000.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention is directed to a tangent-space painting system,offering a high degree of predictability as a brush conforms to anunderlying surface curvature. More particularly, the present inventionrelates to a tangent space brush that paint directly onto the surface ofthe three dimensional (or higher) object, providing an easy way for auser to paint directly onto a three dimensional object, without havingto manipulate a corresponding 2D texture.

2. Description of the Related Art

Typically, when creating virtual 3D objects, it is common to apply 2Dimages to a 3D surface, helping to simulate the appearance of a realobject. This technique, known as texture mapping, provides indirectcontrol over the material parameters of the surface, such as color,shininess, roughness, or even geometrical properties like bumps. Thetechnique known as 3D painting strives to provide direct control overthe appearance of the surface. However, a number of technologies arerequired to support the simulation of painting on a three dimensionalphysical object using a 2D input device.

The 3D objects used in 3D paint systems are typically “parametricobjects.” The mathematical definition of a parametric object would beany piece of geometry defined as a collection of subsets of ann-dimensional space, where each subset can be represented by a pvariable function F:

F: R pR n

(s, t, . . . )F(s, t, . . . )

In the case of a 3D object, p=2, n=3, and F is the texture mappingfunction. For a 3D object, we say that the 3D object is a parameterizedobject, which “lives” in 3D space.

For relatively flat surfaces, and when parameterization is uniform,texture mapping is simple using 2D paint software or scan data. In thesecases, manipulating the texture indirectly in 2D suffices. However, incomplex scenes and on complex characters, only direct manipulationoffers enough usability to achieve the desired results. In typicalnon-trivial scenes, parameter-space is severely distorted or thegeometry shape or topology is unworkable with indirect methods. 3Dpainting offers direct manipulation by managing non-intuitive mappingsfor the user.

Several systems simply use a 2D painting system and periodically projectthe digital painting back onto the 3D object “beneath” the painting.This technique is called screen-space projection as the user effectively“paints” on the screen, which is projected onto a 3D object displayed“behind” the screen. While this approach works well when the objectbeing painted is quite flat and facing the screen (like a piece of paperplaced on the screen), it works quite poorly on objects that curve awayfrom the screen (like a sphere) as the projection process smears thepainting across the surface. This problem can also be viewed as brushdistortion, e.g. a circular brush will produce a distorted ellipticalsmear of paint on a surface, which moves (or is angled) away from thescreen. 3D objects with a complex shape, or complex topology, furthercomplicate the use of a screen-space system due to the restrictions ofsuch a simple projection.

For example, FIGS. 1A and 1B illustrate a prior art method of painting a3D sphere. FIG. 1A illustrates a three dimensional sphere 100 comprisedof polygons. FIG. 1B illustrates a “texture space”, which is a 2Dtexture space corresponding to the sphere illustrated in 3D.

Suppose a user wants to paint a checkerboard pattern onto the sphere.The user can copy a standard checkerboard pattern 101 onto the 2Dtexture space illustrated in FIG. 1B. Thereafter, the texture spaceillustrated in FIG. 1B can be projected onto the sphere 100 asillustrated in FIG. 1A.

However, directly transposing the pattern on the 2D texture space ontothe 3D sphere results in distortions. For example, see the top pole area102 of the sphere illustrated in FIG. 1A, which illustrates severedistortions (a swirl appearance) of the checkerboard pattern.Furthermore, the checkerboard square patterns are mapped into long orthin rectangles on the sphere, depending on how far they are from theequator. This was not originally intended.

Other prior art approaches to this problem would perform complexcomputations onto the already painted 2D texture space to intentionallydistort the 2D space (to match the 3D shape) before projecting it ontothe 3D shape. However, such approaches are burdensome for the user andtime consuming, and also subject to a host of other practical problemsincluding problematic reassembly of the different pieces. On complexobjects, this is not even possible to achieve.

Therefore, what is needed is a system that allows a user to paintdirectly onto the surface of a parametric object living in threedimensions or higher, thereby allowing a user to easily paint on a 3Dsurface without concern for distortion and without having to first paintin the 2D texture space.

SUMMARY OF THE INVENTION

It is an aspect of the present invention to provide a system that allowsa user to paint directly onto a parameterized (or n-dimensional)surface.

It is another aspect of the present invention to provide a system thatallows a user to paint using a volumetric brush instead of a flat brush.

It is an additional aspect of the present invention to provide a systemthat allows a user to paint directly onto a surface of a parametricobject using a procedural brush (for example a filter).

It is yet a further aspect of the present invention to provide a systemthat paints while determining and using a brush defined with anappropriate brush resolution.

It is also an aspect of the present invention to render textures on asurface while reducing artifacts.

It is yet another aspect of the present invention to provide additionalfeatures and improvements to parametric painting systems than presentlyavailable in the prior art.

The above aspects can be attained by a system that includes selecting anarea of a displayed parametric object living in three dimensional orhigher space; and painting a brush directly onto a surface of the area.

More particularly, the above aspects can be attained by a system thatimplements a “tangent space brush.” A tangent space brush is firstpositioned onto a surface using any conventional input device. Forexample, 3D input devices define a point in space, which can beassociated with the closest point on the surface. 2D input devices likea tablet or a mouse can define a point on the surface by intersectingthe view ray that goes through the current screen location with the 3Dsurface. Any other method to interactively define a point on the surfaceis equally valid.

The brush is then aligned with the tangent space at the said surfacelocation, so that the brush normal equals the local surface normal. Thetangent space mapping is defined by the projection along the brushnormal. Each point P(x, y, z) of the surface corresponds to a point B(s,t, h) in the brush space (where s and t lie in the tangent space, and his measured along the normal). The point P is also associated with apoint T(u, v) in texture space, using conventional texture coordinates.

These together with other aspects and advantages which will besubsequently apparent, reside in the details of construction andoperation as more fully hereinafter described and claimed, referencebeing had to the accompanying drawings forming a part hereof, whereinlike numerals refer to like parts throughout.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A illustrates a three dimensional sphere comprised of polygons;

FIG. 1B illustrates a “texture space”, which is a 2D texture spacecorresponding to the 3D sphere illustrated in FIG. 1A;

FIG. 2A illustrates one example of painting directly onto a 3D surface,according to one embodiment of the present invention;

FIG. 2B illustrates the 2D texture space corresponding to the sphereillustrated in FIG. 2A, according to one embodiment of the presentinvention;

FIG. 3A illustrates another example of painting directly onto a 3Dsurface, according to one embodiment of the present invention;

FIG. 3B illustrates the 2D texture space corresponding to the sphereillustrated in FIG. 3A, according to one embodiment of the presentinvention;

FIG. 4 is a block diagram illustrating three different areas of memorythat store the 3D space, the texture space, and the stamp intermediatespace, according to one embodiment of the present invention;

FIG. 5A is a block diagram illustrating concepts used in painting on a3D surface;

FIG. 5B illustrates the concept of an interpolated normal vector;

FIG. 6 illustrates one possible example a tangent space cursor,according to one embodiment of the present invention;

FIGS. 7A, 7B, 7C and 7D illustrate in more detail how painting directlyon a 3D surface is accomplished, according to one embodiment of thepresent invention.

FIG. 8 illustrates the projection of a surface to the tangent plane,according to one embodiment of the present invention;

FIGS. 9A and 9B illustrate painting of a sphere with a circular stamp,according to one embodiment of the present invention;

FIGS. 10A and 10B also illustrate the sphere of FIGS. 9A and 9B,according to one embodiment of the present invention;

FIGS. 11A and 11B illustrate the results of using a two dimensional anda three dimensional stamp, according to one embodiment of the presentinvention;

FIGS. 12A and 12B illustrate a top view of FIG. 11A and the texturespace, respectively, according to one embodiment of the presentinvention;

FIGS. 13A and 13B illustrate another example of normal clipping, and thetexture space, respectively, according to one embodiment of the presentinvention;

FIG. 14 illustrates how a stamp can be rotated in the direction applied,according to one embodiment of the present invention;

FIG. 15 is a block diagram illustrating the process of painting intangent space, according to one embodiment of the present invention;

FIG. 16 illustrates a two dimensional texture map 1600, but which usesdifferent resolutions, according to one embodiment of the presentinvention;

FIG. 17 is a diagram illustrating a first operation for coloringbackground overscan pixel, according to one embodiment of the presentinvention;

FIG. 18 is a diagram illustrating a second operation for coloringbackground overscan pixels, according to one embodiment of the presentinvention;

FIG. 19 represents a flowchart for implementing one embodiment of theoverscanning process described above;

FIG. 20 is a flowchart illustrating one method of applying a proceduralbrush directly onto a three dimensional surface, according to oneembodiment of the present invention; and

FIG. 21 is a block diagram illustrating one example of a sampleconfiguration of hardware used to implement the present invention,according to one embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention is directed to a system that allows a user topaint directly onto a surface of a parametric object (for example a 3Dobject), without concern for distortion caused by projecting from a 2Dtexture space.

While the description herein generally describes and illustratesparametric objects living in three dimensions, the present applicationis applicable to n-dimensional surfaces (where n is any number). Forexample, an animated object can be considered as a four dimensionalsurface (x, y, z, time). All of the concepts described herein can beapplied to any number of dimensions using conventional methods such asdifferential geometry.

FIG. 2A illustrates one example of painting directly onto a 3D surface.The image of FIG. 2A was created by starting with a plain white sphere201. The sphere can be created by using any known three-dimensionalsurface creation technique, for example subdivision surfaces, NURBS,polygons, etc. In this particular example, a circular black brush (or“stamp”) was chosen, but any defined stamp/color can be used. Theletters “Hi!” 200 were painted directly onto the sphere 201 of FIG. 2Aby using a mouse, although any input device can be used. FIG. 2Billustrates the conventional 2D texture space corresponding to thesphere 201 illustrated in FIG. 2A. Note the distortion of the letters“Hi!” 202 in FIG. 2B. According to the present invention, since the userpaints directly onto the three-dimensional surface illustrated in FIG.2A, the user is not required to be concerned with the 2D texture space.

Note that the image displayed in FIG. 2A is view independent. In otherwords, the user can choose any arbitrary angle to view the image thatthe user desires, and the three dimensional image is constructedaccordingly. Either the viewpoint can be changed, or the image rotatedas desired by the user.

FIG. 3A illustrates another example of painting directly onto a 3Dsurface. The image of FIG. 3A was created by starting with a plain whitesphere 301. A circular black brush (or “stamp”) was chosen. Thecheckerboard pattern 300 was painted directly onto the sphere 301 byusing a typical two-dimensional mouse. FIG. 3B illustrates the 2Dtexture space corresponding to the sphere illustrated in FIG. 3A. Again,as in FIG. 2B, note the distortion of the checkerboard pattern 303 intexture space in FIG. 3B, compared to the image of FIG. 3A.

FIG. 4 illustrates three different areas of memory stored in a computerthat store the 3D space 400, a stamp intermediate space 402, and atexture space 403, where the 3D space 400 stores the 3D object, in thiscase a sphere 404, typically comprising polygons. The 3D object can bemade using any method of making 3D object, for example (but not limitedto) subdivision surfaces and NURBS. A triangle shape 405 is painted ontothe sphere 404. These areas in memory store these items asconventionally done using a conventional 3D paint program.

The stamp intermediate space 402 stores the actual shape of the stamp(or brush). The shape of the stamp can be any shape, such as square orround, and can be “transparent” except for the actual pixels used sothat when the stamp is applied (or projected) any remaining textureassociated with a transparent area of the stamp remains the same. Aplurality of different stamps can be created and stored in memorysimultaneously. This particular stamp 406 stored in the stampintermediate space 402 has a triangle shape.

The texture space 403 stores textures to be mapped onto the 3D sphere405. A triangle texture 408 is mapped onto the triangle 405 on thesphere 404. The texture space 403 corresponds to what is illustrated ineither of FIG. 2B or 3B.

FIG. 5A is a block diagram illustrating concepts used in painting on a3D surface. A circle 500 exists in two-dimensional space, and a tangentplane 506 intersects the circle 500 at a hit point 502 in the circle500. Also illustrated is a normal 504 to the hit point 502. The tangentplane 506 is perpendicular to the normal 504. A stamp (or brush) can beprojected onto the tangent plane to paint on the circle (more on theprojection below). While FIG. 5A is illustrated in two dimensions, thesame concepts are applied using the normal 504 in three dimensions inthe present invention.

FIG. 5B illustrates the concept of an interpolated normal vector. In theforthcoming description, when a normal vector is computed it can eitherbe a standard normal vector, or an interpolated normal vector. In somecases, an interpolated normal vector is used to improve accuracy. Points510, 511, 512, and 513 define three connected lines which can representthe underlying polygonal surface onto which paint is to be applied, orthe points can represent vertices for a spline curve based surface suchas a NURBS surface. The standard normal vector computed at an arbitrarypoint 517 would be normal vector 518. This is because point 517 lies onthe line between points 511 and 512, of which the normal vector 518would be perpendicular to the line. On the other hand, an interpolatednormal vector can provide a more accurate normal vector for purposes ofprojections onto a NURBS surface. The interpolated normal vector 520points closer to the bottom because the interpolated normal vector 520is closer to point 512 then point 511. An interpolated normal vector canbe computed in numerous conventional ways, in either 2D or 3D.

In order to paint on a three-dimensional surface, first an input deviceinputs coordinates. These coordinates are projected to the world-spacepoint on a surface of the 3D object. A normal is determined at thatpoint and a brush image, positioned on a tangent plane, is essentiallyprojected to that point, along the normal, onto the underlying surfaces.Thus, a user can paint using a “tangent space cursor” on the surface ofa 3D object.

FIG. 6 illustrates one possible example a tangent space cursor. A 3Dsphere 600 is pictured. The user, by manipulating a 2D pointing devicecan point to points in 3D space (not pictured), and a normal vector 602and a tangent space 604 defined by the size of the brush can becomputed. The curved surface under the tangent space 604 is painted.

FIGS. 7A, 7B, 7C and 7D illustrate in more detail how painting directlyon a 3D surface is accomplished, according to one embodiment of thepresent invention.

FIG. 7A illustrates a 3D sphere 701 and a selected x, y coordinate. Thex, y coordinate is on a screen plane 703, from which a camera point 707views the sphere 701.

FIG. 7B illustrates that the selected (x, y) coordinate 700 is mapped toa 3D screen space point P(x,y,z) 702. The mapping is made by a lineartransformation of the input device coordinates to screen-spacecoordinates, and then the screen space coordinates are mapped to the 3Dviewing frustum.

FIG. 7C illustrates a ray 704 that is generated into the frustum. Theray 704 is formed by connecting a viewpoint V(x,y,z) 705 with the screenspace point P(x,y,z) 702 and it is tested for intersection with thesphere 701. The closest 3D intersection point Q (x,y,z) 706 (or hitpoint) is calculated.

FIG. 7D illustrates a normal 708 to the intersection point Q(x,y,z) 706.A normal to the intersection point Q(x,y,z) 706 is calculated whichdetermines the tangent plane 710 which is perpendicular to the normal708 and intersects the intersection point 706 Q(x,y,z). The normal thatis calculated can also be an interpolated normal (as discussed above).The paint stamp or brush is positioned on the tangent plane 710.

To paint the polygonal surface of the 3D object, the polygons that lieunder (or within the area of influence of) the brush need to bedetermined and the part of the polygons covered (or to be painted) bythe brush determined. To do this the system defines a tangent planebrush using the tangent plane and the brush radius (and depth) mappedinto the tangent plane. The polygons of the surface are then identifiedby projecting the polygons to the tangent plane. Portions fallingoutside of the world-space brush are identified and essentially clippedby applying the tangent plane normal's inverse transformation to thevertices. This simplifies the projections by the vertex-z value becomingzero. Note that S and t define the projection into the tangent space, hthe distance to the plane. For a single point, clipping happens when (s,t) are outside the brush radius (or fall into a fully transparent areaof the brush) or when h exceeds the brush depth. For a triangle,clipping happens when all points in the triangle are clipped. A simpleconservative test using only bounding boxes calculations can be used toquickly reject invalid triangles.

FIG. 8 illustrates the projection of a surface to the tangent plane. Thetangent plane pattern 800 can be rendered into the object's texturespace using the texture coordinates specified by the projected trianglefrom the object's original texture mapping, for each projected triangle(or other polygon). After the polygons under the brush to be painted aredetermined (as discussed above), they can be rendered by mapping thebrush texture onto the surface texture. For triangles, this is a simpleconventional mapping. Solving the texture mapping problem using atangent space brush amounts to layered texture mapping from the brushtexture to the surface texture. A number of methods can be used for thismapping, and the mapping can utilize any existing triangulation. Thetriangles can then be converted pre-computed barycentric coordinates.Using point sampling, a conventional fast feedback version of thetexture can be supplied.

Note that typically, the brush should typically be small with respect tothe curvature of the surface. Otherwise, the brush may be distorted whenit is mapped via the tangent plane normal to the surface.

FIGS. 9A and 9B illustrate the painting of a sphere 900 with a circularstamp. FIG. 9A illustrates the sphere 900 painted with one applicationof a circular stamp. The stamp is placed directly in front (or where theviewpoint is) of the sphere 900. FIG. 9B illustrates the texture spacemapping of the sphere illustrated in FIG. 9A. In this example, the stampcovers the pole of the sphere, where the texture coordinates introduce alot of distortions and some discontinuities. Previous art methods couldnot easily paint a round brush on the sphere. Notice how the texture 9Bmust me distorted to produce the correct round stamp.

FIGS. 10A and 10B also illustrate the sphere 900 of FIGS. 9A and 9B.FIG. 10A illustrates the sphere painted as described above with regardto FIG. 9A, but from a different viewpoint (or in the alternative afterrotation of the sphere). FIG. 10B illustrates the texture space of FIG.10A.

FIG. 10A illustrates how (in one embodiment of the present invention),the normal vector of the surface being painted can affect the intensityof the paint applied to the surface. The center of the applied stamp1000 is dark black, while the edges 1002 are gradually lighter. Thiseffect can be used to increase the realism of the application of thestamp.

By analogy, spraying spray paint directly onto a sphere would produce asimilar effect. The intensity of the paint can be gradually variedresponsive to the angle between the tangent plane normal and the surfacenormal. For example, the intensity can be inversely proportional to theangle between normals. Where the paint is the lightest on the sphere1002, the difference in normal vectors of the surfaces of the sphere anda hit point normal vector approaches 90 degrees. When the difference innormal vectors is greater than 90 degrees, painting on the surface canstop completely. One particularly intuitive mode consists in paintingwith full intensity for angles below a certain threshold A, andprogressively using less paint when angle varies between A and 90degrees. Parameter A can be set to adjust the desired effect. Many otherresponse functions that map the angle to an intensity factor between 0and 1 could be used also.

Brushes (or stamps) can also be three dimensional instead of the typicaltwo-dimensional stamp. A three dimensional shape of a brush can becylindrical, although they can be made into other three dimensionalshapes as well, such as spherical, rectangular, or any arbitrary threedimensional shape. The simplest implementation consists in a singlebrush image I(s, t) and a profile curve d(h), defining a generalizedcylinder. The profile curve determines the depth of the volumetricbrush. The paint intensity is defined by the product I(st)d(h). Anintuitive profile curve could be a smooth function which is 0 outside ofand a smooth interpolation in and Using a three dimensional brush canresult in more realistic effects when painting directly onto a threedimensional surface. Parts of the 3D surface may be painted even whenfar for the brush center, because they would project close to the centerof the brush. This is unintuitive for most users, and defining a finitebrush depth solves the problem.

FIGS. 11A and 1B illustrate the results of using a two dimensional brushand a three dimensional brush. FIG. 11A illustrates a folded threedimensional surface 1100 with a first area 1102 painted by a flat roundstamp and a second area 1104 painted by a volumetric cylindrical stamp.FIG. 11B illustrates the texture space for the surfaces illustrated inFIG. 11A.

Note how the second area 1104 painted by the cylindrical brush comes outalmost rectangular, and avoids the large leakage visible in 1102. Thisis because we set the depth value to be small to build a very flatcylinder, and thus clipped the parts of the surface away from thetangent plane. However, note that the edges 1106 of the second areaappear lighter before the edges are completely clipped. This is moreeasily seen in FIG. 11B, wherein the edges 1108 of the second area 1104appear lighter. This is because, as discussed above, the intensity ofthe stamp projection can vary depending on the normal vector of thesurface being painted.

FIGS. 12A and 12B illustrate a top view of FIG. 11A and the texturespace, respectively. The first area 1200, painted by the two dimensionalbrush, was painted from the same angle as the viewpoint in FIG. 12A. Theround (or cylindrical) shape of the stamp can be clearly seen. Thesecond area 1202, painted by the three dimensional stamp, appearsrectangular because of the distance clipping described above.

Thus, using a three dimensional brush allows a user to paint directlyonto the three-dimensional surface, while producing a more preciseeffect than a two dimensional brush.

FIGS. 13A and 13B illustrate another example of normal clipping, and thetexture space, respectively. The brush used to create the area painted1300 on the top surface 1302 could have either been a two dimensionalbrush or a three dimensional cylindrical brush, as the effect wouldtypically be the same In this case, the difference in normal between thehit point normal of the top surface (where the paint is applied) and anormal at an edge 1303 of the surface is very sharp, sharper than acorresponding angle in FIG. 1A. In the case of FIG. 13A the differencebetween normals is greater than 90 degrees, and the clipping stops theprojection of the stamp entirely. Thus, unlike the result in the firstarea 1200 of FIG. 11A, the stamp does not get projected onto the bottomsurface 1304. This is so, even though the normal of the bottom surface1304 is similar to the hit point normal where the paint is applied.Parameters can be adjusted so that the paint would not be clipped on thebottom surface 1304, if the user so desires. In FIG. 11A, the differencebetween the hit point vector and the surface normal vector did not varyby more than a predetermined amount (in this case 90 degrees). As such,the intensity of the paint was lightened in the intermediate region 1106where this difference approached 90 degrees, but painting was neverstopped completely. In contrast to FIG. 11A, in the case of FIG. 13A,because of the sharp change in normal vectors, the projection of thepaint of the brush is stopped entirely.

FIG. 13B represents the texture space of FIG. 13A. Note that theintensity of the paint is lightened in the region before the projectionof the brush is completely stopped. This can be more easily seen in FIG.13B, where an edge region 1306 is lighter. The brief lighter region isdue to the change in normal vector before the clipping stops projectionof the brush entirely. The intensity can be computer by using a degree 3polynomial: if a is the angle and a0 is the threshold angle, then ifa<a0, then I(a) 1; if I(a)>90, then =0; otherwise I(a)=f(a)/f(a0), withf(a)=(90−a)*(90−a)*(a+(a0+90)/2). Any I(a) function can be used,although I(a)=1 is a simple smooth one.

FIGS. 14A and 15B illustrate how a brush (or stamp) can be rotated tomatch the direction that the brush is moving. In another embodiment ofthe present invention, a brush (whether two or three dimensional) can berotated along the normal to follow the direction the stroke is applied.

When a stamp is projected onto a surface, it is typically aligned aroundthe normal vector of the surface onto which it is projected, in orderfor it to be properly painted onto the surface. Areas1402,1404,1406,1408, and 1410 were all made in one stroke.

However, the stamp can also be rotated in an arbitrary direction aroundthe normal vector, in effect “pointing” the stamp in a particulardirection on the three dimensional surface. The direction the stamp isrotated to match or relate to the direction an arbitrary stroke is beingapplied. Areas 1412, 1414, 1416, 1418, 1420, 1422, and 1424 were allmade in one stroke. However, in this case, the rotation of the stampcorresponds to the direction of the stroke. In this case, the strokestarts out going in the rightmost directions (90 degrees) and then headsdownwards (180 degrees). The rotation of the stamp is adjusted to matchthe direction of the stroke.

The brush stroke direction can be obtained by connecting the differentbrush centers on the 3D surface. This defines a curve on the surface.The tangent vector to this curve is contained into the tangent plane byconstruction, and can be used as the s direction of the brush referenceframe.

FIG. 15 is a block diagram illustrating the process of painting intangent space, according to one embodiment of the present invention.

The process starts 1500 by performing any initialization that may berequired. The process then inputs 1502 two dimensional devicecoordinates, typically from a pointing device, such as a mouse. Theprocess then scales and translates 1504 the 2D coordinates into screencoordinates. Then, the process maps 1506 the coordinates onto the 3Dviewing window resulting in P(x,y,z) (a three dimensional coordinate).

After the mapping, the process conventionally projects 1508 a ray into aviewing volume from P(x,y,z). Any conventional mathematical method canbe used to accomplish this projection. The process then intersects 1510the ray with objects in the viewing volume. This can be accomplished bydetermining Q (which is on the object), the closest point to P, andreject any other intersections. The intersection object can be labeledas B.

Next, the process calculates 1512 the normal at Q (which specifies thetangent plane). K is determined, which is defined as the bounding box onthe tangent plane of the brush texture, which will be drawn to thesurface. K is determined depending on the brush radius and orientation.If a 3D cylindrical brush is used, the cylindrical brush can be definedas including both a brush radius (in world space) and a brush depth (inworld space).

Subsequent to the calculating, the process tessellates 1514 (ifnecessary) the 3D object to triangles and ensures that the triangleshave corresponding texture coordinates. The 3D object can be any 3Dobject, such as a subdivision surface or a NURBS surface, which can thenbe tessellated.

After the tessellating, the process loops 1516 over all triangles T inthe object B. The process checks 1518 to see if the distance fromtriangle T to P is greater than the brush depth, for each triangle inobject B. If the distance is greater, then this triangle is clipped (notrendered) and the process returns to the looping 1516 for the nexttriangle. If the distance is not greater, the process then checks 1520to see if T is facing in an opposite direction to the direction of thetangent plane is facing. If T is facing in an opposite direction, thetriangle is clipped and the process proceeds back to the looping 1516operation for the next triangle.

From the checking, if T is not facing in an opposite direction, then theprocess projects 1522 the triangle T to the tangent plane resulting inS. S is used as the texture coordinates of the brush texture and usesthe existing texture coordinates associated with T. The projection canbe performed by any conventional method.

After projecting, the process then clips 1524 S against K (the boundingbox on the tangent plane). This is the case where a portion of trianglefalls inside the brush, and a portion falls outside the brush. Only theportion of the triangle that falls inside the brush inside will bepainted.

Next, the process checks 1526 to see if there is an intersection. Ifthere is no intersection, then the process proceeds to the looping 1516operation and loops to the next triangle.

If the checking 1526 determines that there is an intersection, then theprocess renders 1528 the brush texture from S to T A conventionalrenderer can be used to render the brush texture. More on the renderingprocess will be discussed below.

After the rendering, the process checks 1530 to see if there are moretriangles. Either only the triangles connected to the painted ones areconsidered, or all triangles of the object. The first mode results infaster paint loop, and ensures that a stamp is always painting aconnected piece of the 3D surfaces. The second mode is easier toimplement, and can be more accurate when the surface is made of severaldisconnected pieces. If more triangles are found, the process returns tothe looping 1516 operation that loops to the next triangle. If thechecking 1530 operation determines that there are no more triangles, theprocess then stops 1532 that finishes the process.

With regard to the rendering 1528 operation, which renders the brushtexture from S to T, this operation comprises sub-operations 1536-1542.The sub operations determine 1536 the brush texture size needed (more onthis below). Then the process determines 1538 which (if any) triangleedges require overscan (more on this below). The process then performs1540 scanline rendering. The process then ends 1542, which terminatesthe rendering process.

In an additional embodiment of the present invention, the brush texturesize can be determined and possibly adjusted depending on the resolutionof the surface being painted. FIG. 16 is a diagram illustrating oneexample of a situation where the brush texture size should be changed.

FIG. 16 illustrates a two-dimensional texture map 1600, but one whichuses different resolutions. For example the left most side is made of2.times.2 pieces 1602,1606, while the rightmost side is made of4.times.4 pieces 1604 1608. Different resolutions are sometimes usedwhen certain parts of a surface need to be more detailed than otherparts. A 2.times.2 brush 1610 and a corresponding 4.times.4 brush 1612are illustrated in FIG. 16.

Note that the left most pieces 1602,1606 can properly be painted usingthe 2.times.2 brush 1610. However, using the 2.times.2 brush 1610 topaint the right most pieces 1604, 1608 could cause problems. If the2.times.2 brush 1610 were applied directly to the right most pieces1604, 1608 (without any scaling), then the size of the brush afterpainting would be reduced on the right, which may not be what the userintended. If the brush were projected to properly match the resolutionof the texture being painted on to preserve the physical size of thebrush, in some cases the enlargement would cause the brush to lookchunky or distorted. In other words, a lower resolution brush may paintfine on a lower resolution grid, but the same lower resolution brush maylook chunky on a higher resolution grid.

Therefore, the resolution of a brush being used should be compared tothe resolution of the texture being painted. If the brush resolution issmaller than the texture resolution, any resultant projections mayappear chunky. Thus, an appropriately sized brush (from FIG. 15,operation 1536) is determined. One way this determination can be made isby matching the brush resolution to be at least the resolution of thetexture. A table can be used to store different brush resolutions of thesame brush image. A custom brush size image can also be made by startingwith a resolution higher than is needed and conventionally resizing thedimensions downward as needed. When the resolution of a brush defined byan image needs to be increased, bilinear interpolation or even aMitchell filter can be used. For procedural brushes, an image at theright resolution can be produced from its definition.

In an embodiment of the present invention, overscan techniques can beused to prevent or reduce artifacts. Sometimes, a pixel may liepartially inside and partially outside of an object surface boundary,causing artifacts. See U.S. Pat. No. 6,037,948, for a more detaileddiscussion of this problem.

Depending on the rendering technique used, pixels partially inside thesurface or even completely outside the surface will contribute in thefinal rendered color. Texture point sampling will use any pixel at leastpartially covered, bilinear interpolation will also use all theneighbors of the set of pixels defined above. Those two cases areaddressed by U.S. Pat. No. 6,037,948. When conventional mip-mappingrendering is used, all pixels may contribute, including the onearbitrary far from the painted areas. It is thus important that allthose background pixels are assigned with an appropriate color.

FIG. 17 is a diagram illustrating a first operation for coloringbackground pixels after conventional overscan. Block 1700 illustrates a4.times.4 grid with background pixels designated by a “” First, theMIPMAP levels are computed keeping track of the background pixels.

Block 1702 illustrates a second level for coloring background pixels.Four pixels from the previous level (1700) correspond to one pixel atthis level. If the 4 corresponding pixels at the previous level arebackground pixels, the new pixel is also a background pixel. Otherwise,the color is the average of the non-background pixels.

Block 1704 illustrates a third level for coloring background overscanpixels. The color is the average of the previous non-background pixels.

FIG. 18 is a diagram illustrating a second operation for coloringbackground overscan pixels.

Block 1804 represents the color computed from block 1704 in FIG. 17(w=Block 1802 represents a traversal of the second level of the MIPMAPin the other direction, this time assigning w to only the backgroundpixels illustrated in block 1702 of FIG. 17. Otherwise, the previouslycomputed pixel values (block 1702) remain the same. In block 1802, x=a,y=((b+e+f)/3) and z=((c+d+g+h)/4). Block 1800 represents the traversalback to the first level of the MIPMAP. Any background pixels from block1700, FIG. 17, are given the corresponding coarser level values fromblock 1802. For example, from block 1700 from FIG. 17, the upper leftmost 4 pixels are background pixels, so they are colored with color wfrom FIG. 18, block 1802. The pixel at column 1, row 3 of block 1800 isalso designated as a background pixel in block 1700, therefore it iscolored with the corresponding color y from block 1802. The remainingbackground pixels from block 1700 are colored with color x. Thenon-background pixels are unchanged.

The result of the above-described background filling process is that aconventional MIPMAP algorithm will then produce the correct result,without having to distinguish painted from background pixels. Inparticular, conventional hardware can be used without any backgroundcolor leakage happening along the texture seams as coarser levels of theMIPMAP are used.

FIG. 19 represents a flowchart for implementing one embodiment of theoverscanning process described above. The process first starts 1900 withan initial MIPMAP (i.e. FIG. 17, item 1700).

The process then creates 1902 a subsequent MIPMAP level. The method usedin the example above assigns or correlates four pixels in the previouslevel to one pixel in the next level, and assigns each pixel to theaverage of the non-background pixels. The assigning could be considereda “consolidating” of pixels, in other words assigning one pixel to aplurality of corresponding pixels.

The process then checks 1904 to see if any background pixels are left inthe newly created level. If there are background pixels left, then theprocess returns to create 1902 another subsequent MIPMAP level.

If there are no background pixels left, then from the checking 1904, theprocess then reverse maps 1906 to the previous MIPMAP level (for exampleas illustrated in FIG. 18). The process then checks 1908 to see if theprocess is currently at the original level. If not, then the processcontinues to reverse map 1906.

If the checking 1908 operation determines that the process has reachedthe original level, then the process ends 1910. Assuming that at leastone pixel was painted, no background pixels should now be in the newlycreated MIPMAP.

In another embodiment of the invention, an “effect brush” can be used topaint on a 3D surface. An effect brush is one for which an algorithm isapplied to the surface. The brush can use a predefined filter (oreffect) and/or perform an active process on an area to be painted.Effect brushes have commonly been used in two-dimensional paintingprograms. Examples of known effect brushes include blur, smear, soften,sharpen, solarize, etc.

The present invention allows a user to paint directly on a threedimensional surface using an effect brush. Thus, the user can easilyapply special effects and brushes directly and easily onto a threedimensional surface.

FIG. 20 is a flowchart illustrating one method of applying an effectbrush directly onto a three dimensional surface. The method firstdetermines 2000 the bounding box on the tangent plane to be painted,typically in the same way as illustrated in FIG. 15.

The process then reverse renders 2002 pixels from the three-dimensionalsurface inside the bounding box to an area in memory. The process thenapplies 2004 a predetermined procedure or filter to the area in memory(i.e. blur, soften, etc.)

After the applying 2004, the process then renders 2006 the pixels in thearea in memory back onto the same bounding box on the three dimensionalsurface.

FIG. 21 is a block diagram illustrating one example of a configurationof hardware used to implement the present invention.

A display monitor 2100 is connected to a computer 2102. The computerperforms the operational processes described herein based upon inputfrom a keyboard 2106 and/or a mouse 2108. A drawing tablet 2104 can alsobe connected to the computer 2102. In addition, a drawing pen 2110and/or a puck 2112 can also be used as input devices for the tablet. Ofcourse, any applicable configuration of hardware can be used toimplement the present invention.

The system also includes permanent or removable storage, such asmagnetic and optical discs, RAM, ROM, etc. on which the process and datastructures of the present invention can be stored and distributed. Theprocesses can also be distributed via, for example, downloading over anetwork such as the Internet.

The many features and advantages of the invention are apparent from thedetailed specification and, thus, it is intended by the appended claimsto cover all such features and advantages of the invention that fallwithin the true spirit and scope of the invention. Further, sincenumerous modifications and changes will readily occur to those skilledin the art, it is not desired to limit the invention to the exactconstruction and operation illustrated and described, and accordinglyall suitable modifications and equivalents may be resorted to, fallingwithin the scope of the invention.

1. A method, comprising: selecting an area of a displayed parametricobject living in three dimensional or higher space; and painting a brushtexture map of a volumetric brush directly onto a texture map of asurface of the area of the displayed parametric object in the threedimensional or higher space within a volume of the brush based on brushorientations that minimize a distortion of a painted texture whendisplayed on the surface.
 2. A method as recited in claim 1, wherein thebrush is cylindrical with a defined depth.
 3. A computer graphicsmethod, comprising: selecting an area of a displayed parametric objectexisting in three dimensional space; and painting a brush texture map ofa computer graphics volumetric brush onto a texture map of a surface ofthe area of the displayed parametric object in the three dimensionalwithin a volume of the brush based on brush orientations that minimize adistortion of a painted texture when displayed on the surface.